Any priest (or layman) can use it PRIVATELY, however the authorization of the Ordinary is needed for its public recitation. This from the translation of the Roman Ritual found on EWTN's website. This prayer is for general use--to combat
the power of the evil spirits over a community or locality.
[The following exorcism can be used by bishops, as well as by priests who have this authorization from their Ordinary.]
In the name of the Father, and of the Son, and of the Holy
[Prayer to St. Michael the Archangel]
St. Michael the Archangel, illustrious leader of the heavenly army, defend us in the battle against principalities and powers, against the rulers of the world of darkness and the spirit of wickedness in high places. Come to the rescue of mankind, whom
God has made in His own image and likeness, and purchased from Satan's tyranny at so great a price. Holy Church venerates you as her patron and guardian. The Lord has entrusted to you the task of leading the souls of the redeemed to heavenly blessedness.
Entreat the Lord of peace to cast Satan down under our feet, so as to keep him from further holding man captive and doing harm to the Church. Carry our prayers up to God's throne, that the mercy of the Lord may quickly come and lay hold of the beast, the serpent of old, Satan and his demons, casting him in chains into the abyss, so that he can no longer seduce the nations.
In the name of Jesus Christ, our Lord and God, by the intercession of Mary, spotless Virgin and Mother of God, of St. Michael the Archangel, of the blessed apostles Peter and Paul, and of all the saints, and by the authority residing in our holy
ministry, we steadfastly proceed to combat the onslaught of the wily enemy.
[end--for the rest see www.ewtn.com/library/prayer/